Therefore, one can ask how a quantum error-correction code can be constructed in a heavy-hexagon structure. Constructing a measurement circuit for the syndrome is crucial to implementing a quantum error-correcting code in the heavy-hexagon structure.
Because heavy-hexagon structures have a low-degree connection, the connection restriction requires the use of flag qubit[1]}, [2]}, [3]}, [4]}, [5]}. Moreover, as explained earlier, the characteristic of existing errors, which implies that errors of the Z operator occur more frequently compared to other types, should be considered. Therefore, in this study, we propose a method to construct Tailored Surface code and XZZX code on a heavy-hexagon structure. In particular, we provide a measurement circuit for the syndrome in the tailored surface code and the XZZX code on the heavy-hexagon structure.
